Answer
The free-fall acceleration on the newly discovered planet is $12.25~m/s^2$
Work Step by Step
We can write an expression for the free-fall acceleration on the earth.
$g = \frac{G~M}{R^2} = 9.80~m/s^2$
We can find the free-fall acceleration $g'$ on the newly discovered planet.
$g' = \frac{G~(5M)}{(2R)^2}$
$g' = (\frac{5}{4})~(\frac{G~M}{R^2})$
$g' = (\frac{5}{4})~(9.80~m/s^2)$
$g' = 12.25~m/s^2$
The free-fall acceleration on the newly discovered planet is $12.25~m/s^2$.
